Computational Phylogenomics and Metagenomics Tandy Warnow Departments of Bioengineering and Computer Science The University of Illinois at Urbana-Champaign.

Computational Phylogenomics and Metagenomics Tandy Warnow Departments of Bioengineering and Computer Science The University of Illinois at Urbana-Champaign http://tandy.cs.illinois.edu

The “Tree of Life” Applications of phylogenies to: protein structure and function population genetics human migrations

Challenges: gene tree conflict due to incomplete lineage sorting, horizontal gene transfer, or gene duplication and loss.

1. What is this fragment? (Classify each fragment as well as possible.) 2. What is the taxonomic distribution in the dataset? (Note: helpful to use marker genes.) 3. What are the organisms in this metagenomic sample doing together? Basic Questions

Computational Phylogenetics and Metagenomics Courtesy of the Tree of Life project

Phylogenomic pipeline Select taxon set and markers Gather and screen sequence data, possibly identify orthologs Compute multiple sequence alignments for each locus Compute species tree or network: – Compute gene trees on the alignments and combine the estimated gene trees, OR – Perform “concatenation analysis” (aka “combined analysis”) Get statistical support on each branch (e.g., bootstrapping) Estimate dates on the nodes of the phylogeny Use species tree with branch support and dates to understand biology

Avian Phylogenomics Project (100+ people) G Zhang, BGI Approx. 50 species, whole genomes 8000+ genes, UCEs Gene sequence alignments and trees computed using SATé (Science 2009, Systematic Biology 2012) Concatenation analysis (multi-million site) using ExaML (new version of RAxML for very long alignments) MTP Gilbert, Copenhagen S. Mirarab Md. S. Bayzid UT-Austin UT-Austin T. Warnow UT-Austin Erich Jarvis, HHMI CHALLENGE: Massive gene tree incongruence suggestive of incomplete lineage sorting, but gene trees had poor resolution due to low phylogenetic signal Coalescent-based estimation methods had poor accuracy

1kp: Thousand Transcriptome Project (~40 people) Plant Tree of Life based on transcriptomes of ~1200 species More than 13,000 gene families (most not single copy) Gene Tree Incongruence G. Ka-Shu Wong U Alberta N. Wickett Northwestern J. Leebens-Mack U Georgia N. Matasci iPlant T. Warnow, S. Mirarab, N. Nguyen, Md. S.Bayzid UT-Austin UT-Austin Challenges: 1. Alignment of datasets with > 100,000 sequences, with many fragmentary sequences 2. Gene tree incongruence due to ILS, too many species for standard methods

Ultra-large multiple-sequence alignment (briefly today) Metagenomic taxon identification and abundance profiling Species tree estimation from multiple genes in the presence of gene tree conflict (Math Colloquium, Oct 2) Current Research Projects

Alignment-free phylogeny estimation Supertree estimation Genome rearrangement phylogeny Reticulate evolution detection and reconstruction Data mining techniques to explore multiple optima Theoretical guarantees under Markov models of evolution Historical linguistics Other Research Projects

Phylogenetic Estimation: Big Data Challenges NP-hard problems Large datasets: 100,000+ sequences 10,000+ genes “BigData” complexity missing data mixture models errors in input data model misspecification streaming data

This talk Multiple sequence alignment methods, SATé (2009), PASTA (2014), and UPP (in preparation), and applications to metagenomic taxon identification (TIPP, submitted)

Multiple Sequence Alignment

DNA Sequence Evolution AAGACTT TGGACTTAAGGCCT -3 mil yrs -2 mil yrs -1 mil yrs today AGGGCATTAGCCCTAGCACTT AAGGCCTTGGACTT TAGCCCATAGACTTAGCGCTTAGCACAAAGGGCAT TAGCCCTAGCACTT AAGACTT TGGACTTAAGGCCT AGGGCATTAGCCCTAGCACTT AAGGCCTTGGACTT AGCGCTTAGCACAATAGACTTTAGCCCAAGGGCAT

Phylogeny Problem TAGCCCATAGACTTTGCACAATGCGCTTAGGGCAT UVWXY U VW X Y

AGAT TAGACTTTGCACAATGCGCTT AGGGCATGA UVWXY U VW X Y The “real” problem

…ACGGTGCAGTTACCA… MutationDeletion …ACCAGTCACCA… Indels (insertions and deletions)

…ACGGTGCAGTTACC-A… …AC----CAGTCACCTA… The true multiple alignment – Reflects historical substitution, insertion, and deletion events – Defined using transitive closure of pairwise alignments computed on edges of the true tree … ACGGTGCAGTTACCA … Substitution Deletion … ACCAGTCACCTA … Insertion

Input: unaligned sequences S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC S4 = TCACGACCGACA

Phase 1: Alignment S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- S4 = -------TCAC--GACCGACA S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC S4 = TCACGACCGACA

Phase 2: Construct tree S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- S4 = -------TCAC--GACCGACA S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC S4 = TCACGACCGACA S1 S4 S2 S3

Simulation Studies S1S2 S3S4 S1 = - AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- S4 = -------TCAC--GACCGACA S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC S4 = TCACGACCGACA S1 = - AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-C--T-----GACCGC-- S4 = T---C-A-CGACCGA----CA Compare True tree and alignment S1S4 S3S2 Estimated tree and alignment Unaligned Sequences

Quantifying Error FN: false negative (missing edge) FP: false positive (incorrect edge) 50% error rate FN FP

Two-phase estimation Alignment methods Clustal POY (and POY*) Probcons (and Probtree) Probalign MAFFT Muscle Di-align T-Coffee Prank (PNAS 2005, Science 2008) Opal (ISMB and Bioinf. 2007) FSA (PLoS Comp. Bio. 2009) Infernal (Bioinf. 2009) Etc. Phylogeny methods Bayesian MCMC Maximum parsimony Maximum likelihood Neighbor joining FastME UPGMA Quartet puzzling Etc. RAxML: heuristic for large-scale ML optimization

1000-taxon models, ordered by difficulty (Liu et al., 2009)

Re-aligning on a tree A B D C Merge sub- alignments Estimate ML tree on merged alignment Decompose dataset AB CD Align subproblem s AB CD ABCD

SATé and PASTA Algorithms Estimate ML tree on new alignment Tree Obtain initial alignment and estimated ML tree Use tree to compute new alignment Alignment If new alignment/tree pair has worse ML score, realign using a different decomposition Repeat until termination condition (typically, 24 hours)

1000 taxon models, ordered by difficulty SATé-1 24 hour analysis, on desktop machines (Similar improvements for biological datasets) SATé-1 can analyze up to about 30,000 sequences. SATé-1 (Science 2009) performance

1000 taxon models ranked by difficulty SATé-1 and SATé-2 (Systematic Biology, 2012)

PASTA (2014): even better than SATé-2

1kp: Thousand Transcriptome Project Plant Tree of Life based on transcriptomes of ~1200 species More than 13,000 gene families (most not single copy) Gene Tree Incongruence G. Ka-Shu Wong U Alberta N. Wickett Northwestern J. Leebens-Mack U Georgia N. Matasci iPlant T. Warnow, S. Mirarab, N. Nguyen, Md. S.Bayzid UT-Austin UT-Austin Challenge: Alignment of datasets with > 100,000 sequences with many fragmentary sequences Plus many many other people…

1KP dataset: more than 100,000 p450 sequences, many fragmentary All standard alignment methods we tested performed poorly.

UPP Basic approach: Select random subset of sequences, and build “backbone alignment” Construct a “Family of Hidden Markov Models” on the backbone alignment Add all remaining sequences to the backbone alignment using the Family of HMMs UPP can analyze much larger datasets than PASTA, and is highly robust to fragmentary sequences

One Hidden Markov Model for the entire alignment?

Or 2 HMMs?

Or 4 HMMs?

Impact of backbone size and use of HMM Family technique Notes: Relative performance under standard alignment criteria is not predictive of relative performance for tree estimation. For alignment estimation, a large backbone is important. For tree estimation, the use of the HMM Family is most important, but large backbones also help.

RNASim: alignment error Note: Mafft was run under default settings for 10K and 50K sequences and under Parttree for 100K sequences, and fails to complete under any setting For 200K sequences. Clustal-Omega only completes on 10K dataset. All methods given 24 hrs on a 12-core machine

RNASim: tree error Note: Mafft was run under default settings for 10K and 50K sequences and under Parttree for 100K sequences, and fails to complete under any setting For 200K sequences. Clustal-Omega only completes on 10K dataset. All methods given 24 hrs on a 12-core machine

RNASim Million Sequences: tree error Notes: PASTA cannot run on this dataset size, UPP(Fast,NoDecomp) took 2.2 days, and UPP(Fast) took 11.9 days (both using 12 processors).

Running Time Wall-clock time used (in hours) given 12 processors

Performance on fragmentary datasets of the 1000M2 model condition UPP vs. PASTA: impact of fragmentation Under high rates of evolution, PASTA is badly impacted by fragmentary sequences (the same is true for other methods). Under low rates of evolution, PASTA can still be highly accurate (data not shown). UPP continues to have good accuracy even on datasets with many fragments under all rates of evolution.

Impact of rate of evolution on performance on fragmentary sequence data

New Alignment Methods SATé-1 (Science 2009) can analyze 10,000 sequences SATé-2 (Systematic Biology 2012) can analyze 50,000 sequences, is faster and more accurate than SATé-1 PASTA (RECOMB 2014) can analyze 200,000 sequences, and is faster and more accurate than both SATé versions. UPP (in preparation) uses a very different technique than SATé and PASTA. – Fast – Scalable (up to 1,000,000 sequences) – Robust to fragmentary data

Metagenomic Taxon Identification Objective: classify short reads in a metagenomic sample

Objective: Distribution of the species (or genera, or families, etc.) within the sample. For example: The distribution of the sample at the species-level is: 50% species A 20% species B 15% species C 14% species D 1% species E Abundance Profiling

Leading techniques: PhymmBL (Brady & Salzberg, Nature Methods 2009) NBC (Rosen, Reichenberger, and Rosenfeld, Bioinformatics 2011) MetaPhyler (Liu et al., BMC Genomics 2011), from the Pop lab at the University of Maryland MetaPhlAn (Segata et al., Nature Methods 2012), from the Huttenhower Lab at Harvard mOTU (Bork et al., Nature Methods 2013) MetaPhyler, MetaPhlAn, and mOTU are marker-based techniques (but use different marker genes). Marker gene are typically single-copy, universal, and resistant to horizontal transmission. Abundance Profiling

High indel datasets containing known genomes Note: NBC, MetaPhlAn, and MetaPhyler cannot classify any sequences from at least one of the high indel long sequence datasets, and mOTU terminates with an error message on all the high indel datasets.

“Novel” genome datasets Note: mOTU terminates with an error message on the long fragment datasets and high indel datasets.

TIPP vs. other abundance profilers TIPP is highly accurate, even in the presence of high indel rates and novel genomes, and for both short and long reads. All other methods have some vulnerability (e.g., mOTU is only accurate for short reads and is impacted by high indel rates).

Phylogenetic “boosters” Goal: improve accuracy, speed, robustness, or theoretical guarantees of base methods Techniques: divide-and-conquer, iteration, chordal graph algorithms, and “bin-and-conquer” Examples: DCM-boosting for distance-based methods (1999) DCM-boosting for heuristics for NP-hard problems (1999) SATé- and PASTA-boosting for alignment methods (2009, 2012, and 2014) SuperFine-boosting for supertree methods (2012) DACTAL: almost alignment-free phylogeny estimation methods (2012) SEPP-boosting for phylogenetic placement of short sequences (2012) TIPP-boosting for metagenomic taxon identification (submitted) UPP-boosting for alignment methods (in preparation) Bin-and-conquer for coalescent-based species tree estimation (2013 and 2014)

Warnow Laboratory U Texas PhD students: Siavash Mirarab, Nam Nguyen (former), and Md. S. Bayzid Postdoctoral Fellow: Ruth Davidson (at UIUC) Lab Website: http://www.cs.utexas.edu/users/phylohttp://www.cs.utexas.edu/users/phylo Current and Past Funding: Guggenheim Foundation, Packard Foundation, NSF, Microsoft Research New England, and TACC (Texas Advanced Computing Center). HHMI graduate fellowship to Siavash Mirarab and Fulbright graduate fellowship to Md. S. Bayzid. http://tandy.cs.illiinois.eduhttp://tandy.cs.illiinois.eduTandy’s website

Challenges: Gene tree conflict due to incomplete lineage sorting, duplication and loss, recombination, etc. Reticulate evolution (horizontal gene transfer, hybridization) requiring phylogenetic networks.

Scientific challenges: Ultra-large multiple-sequence alignment Alignment-free phylogeny estimation Supertree estimation Estimating species trees from many gene trees Genome rearrangement phylogeny Reticulate evolution Visualization of large trees and alignments Data mining techniques to explore multiple optima Theoretical guarantees under Markov models of evolution Techniques: machine learning, applied probability theory, graph theory, combinatorial optimization, supercomputing, and heuristics The Tree of Life: Multiple Challenges

Combined analysis gene 1 S1S1 S2S2 S3S3 S4S4 S5S5 S6S6 S7S7 S8S8 gene 2gene 3 TCTAATGGAA GCTAAGGGAA TCTAAGGGAA TCTAACGGAA TCTAATGGAC TATAACGGAA GGTAACCCTC GCTAAACCTC GGTGACCATC GCTAAACCTC TATTGATACA TCTTGATACC TAGTGATGCA CATTCATACC TAGTGATGCA ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Red gene tree ≠ species tree (green gene tree okay)

The Coalescent Present Past Courtesy James Degnan

Incomplete Lineage Sorting (ILS) 1000+ papers in 2013 alone Confounds phylogenetic analysis for many groups: – Hominids – Birds – Yeast – Animals – Toads – Fish – Fungi There is substantial debate about how to analyze phylogenomic datasets in the presence of ILS.

Orangutan GorillaChimpanzee Human From the Tree of the Life Website, University of Arizona Species tree estimation: difficult, even for small datasets

1- Concatenation: statistically inconsistent (Roch & Steel 2014) 2- Summary methods: can be statistically consistent 3- Co-estimation methods: too slow for large datasets Species tree estimation

Is Concatenation Evil? Joseph Heled: – YES John Gatesy – No Data needed to held understand existing methods and their limitations Better methods are needed

Avian Phylogenomics Project (100+ people) G Zhang, BGI Approx. 50 species, whole genomes 8000+ genes, UCEs Gene sequence alignments and trees computed using SATé (Science 2009, Systematic Biology 2012) Concatenation analysis (multi-million site) using ExaML (new version of RAxML for very long alignments) Massive gene tree incongruence suggestive of incomplete lineage sorting -- coalescent-based species tree estimation computed using “Statistical Binning” (Science, in press) MTP Gilbert, Copenhagen S. Mirarab Md. S. Bayzid UT-Austin UT-Austin T. Warnow UT-Austin Erich Jarvis, HHMI

1kp: 1000 Plant Transcriptomes Whole Transcriptomes of 103 plant species and 850 single copy loci (1200 taxa in next phase) Most accurate summary methods cannot handle this size Common ancestor about 1 billion years ago and so gene trees are hard to root Most summary methods need rooted gene trees Pre-existing summary methods do not provide reasonable results on this dataset G. Ka-Shu Wong U Alberta N. Wickett Northwestern J. Leebens-Mack U Georgia N. Matasci iPlant T. Warnow, S. Mirarab, N. Nguyen, UT-Austin UT-Austin UT-Austin Plus many many other people… [Wickett et al. (under review), 2014.]

Our methods “Statistical Binning” (accepted): uses a statistical method to determine sets of “combinable” gene sequence alignments, improves coalescent-based species tree estimation accuracy when gene trees have poor resolution (used for Avian Phylogenomics Project). ASTRAL (Bioinformatics 2014): polynomial time statistically consistent method, can run on very large datasets of unrooted gene trees.

Mammalian simulations Based on a biological mammalian dataset of 37 taxa and 442 genes, published by Song et al., PNAS, 2012. In simulations, we vary – Levels of ILS – Number of genes – Alignment length to control gene tree estimation error Compare ASTRAL to – MP-EST, BUCKy – Concatenation – MRP, Greedy Measure species tree error compared to the known true tree

ASTRAL vs. Concatenation 200 genes, 500bp Less ILS

Analyses of the Song et al. Mammalian dataset The placement of Scandentia (Tree Shrew) is controversial. The ASTRAL analysis agrees with maximum likelihood concatenation analysis of this dataset.

Summary New multiple sequence alignments with improved accuracy and scalability, as well as high robustness to fragmentary data – SATé used in many studies. New coalescent-based species tree estimation methods that have better accuracy than current methods, and can analyze large datasets (used in 1KP and Avian Phylogenomics project analyses) New methods for metagenomic taxon identification and abundance profiling with improved accuracy (will be used in analyses here at Illinois) Method development inspired by collaboration with biologists, and improves biological analyses.

AA Sequence Alignment Error (13 HomFam datasets) Homfam: Sievers et al., MSB 2011 10,000 to 46,000 sequences per dataset; 5-14 sequences in each seed alignment Sequence lengths from 46-364 AA

Alignment Accuracy – Correct columns

Other co-estimation methods Statistical methods: BAli-Phy (Redelings and Suchard): Bayesian software to co- estimate alignments and trees under a statistical model of evolution that includes indels. Can scale to about 100 sequences, but takes a very long time. – http://www.bali-phy.org/ http://www.bali-phy.org/ StatAlign: http://statalign.github.io/ Extensions of Parsimony POY (most well known software) – http://www.amnh.org/our-research/computational- sciences/research/projects/systematic-biology/poy BeeTLe (Liu and Warnow, PLoS One 2012)

Horizontal Gene Transfer – Phylogenetic Networks Ford Doolittle

Warnow Laboratory PhD students: Siavash Mirarab*, Nam Nguyen, and Md. S. Bayzid** Undergrad: Keerthana Kumar Lab Website: http://www.cs.utexas.edu/users/phylohttp://www.cs.utexas.edu/users/phylo Funding: Guggenheim Foundation, Packard, NSF, Microsoft Research New England, David Bruton Jr. Centennial Professorship, TACC (Texas Advanced Computing Center), and the University of Alberta (Canada) TACC and UTCS computational resources * Supported by HHMI Predoctoral Fellowship ** Supported by Fulbright Foundation Predoctoral Fellowship

But… Gene trees may not be identical to species trees: –Incomplete Lineage Sorting (deep coalescence) –Gene duplication and loss –Horizontal gene transfer This makes combined analysis and standard supertree analyses inappropriate

... Analyze separately Summary Method Two competing approaches gene 1 gene 2... gene k... Concatenation Species

... How to compute a species tree?

Statistically consistent under ILS? MP-EST (Liu et al. 2010): maximum likelihood estimation of rooted species tree – YES BUCKy-pop (Ané and Larget 2010): quartet-based Bayesian species tree estimation –YES MDC – NO Greedy – NO Concatenation under maximum likelihood – NO MRP (supertree method) – open

The Debate: Concatenation vs. Coalescent Estimation In favor of coalescent-based estimation – Statistical consistency guarantees – Addresses gene tree incongruence resulting from ILS – Some evidence that concatenation can be positively misleading In favor of concatenation – Reasonable results on data – High bootstrap support – Summary methods (that combine gene trees) can have poor support or miss well-established clades entirely – Some methods (such as *BEAST) are computationally too intensive to use

Results on 11-taxon datasets with strongILS * BEAST more accurate than summary methods (MP-EST, BUCKy, etc) CA-ML: (concatenated analysis) also very accurate Datasets from Chung and Ané, 2011 Bayzid & Warnow, Bioinformatics 2013

Species tree/network estimation Methods have been developed to estimate species phylogenies (trees or networks!) from gene trees, when gene trees can conflict from each other (e.g., due to ILS, gene duplication and loss, and horizontal gene transfer). Phylonet (software suite), has effective methods for many optimization problems – including MDC and maximum likelihood. Tutorial on Wednesday. Software available at http://bioinfo.cs.rice.edu/phylonet?destination=node/3 http://bioinfo.cs.rice.edu/phylonet?destination=node/3

Metagenomic Taxon Identification Objective: classify short reads in a metagenomic sample

1. What is this fragment? (Classify each fragment as well as possible.) 2. What is the taxonomic distribution in the dataset? (Note: helpful to use marker genes.) Two Basic Questions

SEPP SEPP: SATé-enabled Phylogenetic Placement, by Mirarab, Nguyen, and Warnow Pacific Symposium on Biocomputing, 2012 (special session on the Human Microbiome) Tutorial on Thursday.

Other problems Genomic MSA estimation: – Multiple sequence alignment of very long sequences – Multiple sequence alignment of sequences that evolve with rearrangement events Phylogeny estimation under more complex models – Heterotachy – Violation of the rates-across-sites assumption – Rearrangements Estimating branch support on very large datasets

New methods for estimating sequence alignments, gene trees, and species trees, with applications to metagenomics Tandy Warnow Departments of Bioengineering and Computer Science The University of Illinois at Urbana-Champaign http://tandy.cs.illinois.edu

Challenges: gene tree conflict due to incomplete lineage sorting, horizontal gene transfer, or gene duplication and loss.

Phylogenomic pipeline Select taxon set and markers Gather and screen sequence data, possibly identify orthologs Compute multiple sequence alignments for each locus Compute species tree or network: – Compute gene trees on the alignments and combine the estimated gene trees, OR – Perform “concatenation analysis” (aka “combined analysis”) Get statistical support on each branch (e.g., bootstrapping) Estimate dates on the nodes of the phylogeny Use species tree with branch support and dates to understand biology

Phylogenetic Estimation: Big Data Challenges NP-hard problems Large datasets: 100,000+ sequences 10,000+ genes “BigData” complexity missing data mixture models errors in input data model misspecification streaming data

What I do I develop new methods for difficult computational problems, to improve the accuracy of the biological analyses. Collaborations drive method development.

Avian Phylogenomics Project (100+ people) G Zhang, BGI Approx. 50 species, whole genomes 8000+ genes, UCEs Gene sequence alignments and trees computed using SATé (Science 2009, Systematic Biology 2012) Concatenation analysis (multi-million site) using ExaML (new version of RAxML for very long alignments) MTP Gilbert, Copenhagen S. Mirarab Md. S. Bayzid UT-Austin UT-Austin T. Warnow UT-Austin Erich Jarvis, HHMI CHALLENGE: Massive gene tree incongruence suggestive of incomplete lineage sorting, but gene trees had poor resolution due to low phylogenetic signal Coalescent-based estimation methods had poor accuracy

1kp: Thousand Transcriptome Project (~40 people) Plant Tree of Life based on transcriptomes of ~1200 species More than 13,000 gene families (most not single copy) Gene Tree Incongruence G. Ka-Shu Wong U Alberta N. Wickett Northwestern J. Leebens-Mack U Georgia N. Matasci iPlant T. Warnow, S. Mirarab, N. Nguyen, Md. S.Bayzid UT-Austin UT-Austin Challenges: 1. Alignment of datasets with > 100,000 sequences, with many fragmentary sequences 2. Gene tree incongruence due to ILS, too many species for standard methods

This talk Multiple sequence alignment methods, SATé (2009), PASTA (2014), and UPP (in preparation), and applications to metagenomic taxon identification (TIPP, submitted) New coalescent-based species tree estimation methods for: –Avian Phylogenomics Project (submitted) and –1KP, the Thousand Plant Transcriptome Project (submitted)

Phylogenies and Applications Basic Biology: How did life evolve? Applications of phylogenies to: protein structure and function population genetics human migrations

Computational Phylogenetics and Metagenomics Courtesy of the Tree of Life project

Multiple Sequence Alignment (MSA): another grand challenge 1 S1 = -AGGCTATCACCTGACCTCCA S2 = TAG-CTATCAC--GACCGC-- S3 = TAG-CT-------GACCGC-- … Sn = -------TCAC--GACCGACA S1 = AGGCTATCACCTGACCTCCA S2 = TAGCTATCACGACCGC S3 = TAGCTGACCGC … Sn = TCACGACCGACA Novel techniques needed for scalability and accuracy NP-hard problems and large datasets Current methods do not provide good accuracy Few methods can analyze even moderately large datasets Many important applications besides phylogenetic estimation 1 Frontiers in Massive Data Analysis, National Academies Press, 2013